We have inferred the energy distribution of trapped ions in an electron beam ion trap (EBIT) from simulations of the spatial distribution of ${\mathrm{Fe}}^{13+}$ ions and a comparison with measured visible light images of the ion cloud. We simulated the cloud of ${\mathrm{Fe}}^{13+}$ ions by computing ion trajectories in the EBIT for different ion energy distributions used to initialize the trajectories. We then performed a least-squares fit to infer the ion energy distribution that best reproduced the measured ion cloud. These best-fit distributions were typically non-Maxwellian. For electron beam energies of 395–475 eV and electron beam currents of 1–9 mA, we find that the average ion energy is in the range of 10–300 eV. We also find that the average ion energy increases with increasing beam current approximately as $\langle E\rangle \approx 25I_{\mathrm{e}}\mathrm{eV}$, where $I_{\mathrm{e}}$ is the electron beam current in mA. We have also compared our results to Maxwell-Boltzmann-distribution ion clouds. We find that our best-fit non-thermal distributions have an $\langle E\rangle$ that is less than half that of the $T$ from the best-fit Maxwell-Boltzmann distributions $(\langle E\rangle /q)/T=0.41\pm 0.05$.

• Received 21 November 2020
• Revised 7 October 2021
• Accepted 13 December 2021

DOI:https://doi.org/10.1103/PhysRevE.105.015204